Congrats on getting started! You're going to become addicted, and it is going to be awesome. It seems like you're already improving, and your having done a half-marathon will translate well to the Olympic Triathlon distance. That's what you'll be doing for the next LA Triathlon, I take it?
One of the semi-morbid jokes of triathlon is that it's all about who has the most time to train. What to take from that is just that you need to get in every workout you can and focus on quality where you may be short on time. Swims can easily be combined with your bike or run days, and doing one Bike-to-Run workout a week is good. And I would also say that none of your workouts should be less than 20 minutes, and really, never less than 3 miles for runs.
Tips For Swimming:
kennf has it right. It is all about technique. If you don't come from a swimming background, watch a lot of YouTube videos on swim technique. The key elements of any swim stroke which you should be thinking of in the water are head position, body position, arm action, leg action, breathing, coordination, and smoothness and relaxation. Pay attention to what's involved for each of those and apply it in the pool. Do not look at your speed, do not look at the clock. Not yet. Once you can swim 500 meters with perfect technique,
then it's time to speed up. No short-stroking, no water-slapping. Specifically for triathlon I would say that the most important thing is to just
relax. A lot of new swimmers can get tossed around in the start of a triathlon, next comes panic, choking on water, and ruining the rest of your race with a belly full of lake or ocean nasties. When race day comes, be confident that even if every foot and every hand in the water somehow hits you in the face that you are just a calm little dolphin and nothing can phase you.
Tips for the Bike:
Being that this is a bike website I assume you are well-enough on riding technique, but I offer that the bike is the best place to work on your race-day nutrition. Long bike rides can show you what works and what doesn't. For Sprint/Olympic distance you can probably just use a few gel packets or a small gel flask, taking in about 100 calories every 20-30 minutes (find the time-line that works for you). Experiment with different brands to find your favorite. Also make sure to work on bike adjustments for your most comfortable aero position to save your legs for the run. The good thing about biking is that you can also use it for commuting, so if you're having trouble getting workouts in, use your trips to school and work as training sessions.
Tips for the Run:
I would suggest a GPS watch or a pedometer. If GPS is too expensive for now, maybe try a Nike+ iPod or similar device to track your pace. If you have such a device already, pay attention to it more. When racing you really do not want to get used to grabbing onto other peoples' speeds and trying to keep up. That's how you get pace-broken and crash. Learn about your body at different paces and formulate plans based on what could happen during a race. Know your average pace, it's that perfect pace that you can maintain regardless of how many miles you're running.
Transitions:
Transitions are all about rehearsal. If you plan to clip your cycling shoes into the pedals or put them on and run with them to the mount area, it doesn't matter, so long as you know you can do it smoothly. And avoid the picnic area transition. The simpler the better.
T1:
Before you leave the water, add some extra kicking to your swim to get some blood back to your legs, and
think about your plan for getting to and on your bike. I have
everything on my bike, so all I have to do out of the water is put my helmet on and go. And practice how you're going to handle the mount line. This seems silly, but watch some videos of people messing this up:
http://www.youtube.com/watch?v=rjqEogQtVQ0
Remember,
smooth is fast. You should jog to the mount line and pretend like you're in slow motion {on race day it'll still be faster than you think}. It helps to prestage your crank in the high gear with your cassette in the low gear, crank arms parallel to the ground, left pedal forward. Decide if you're going to run through transition with one hand on the seat, or both hands on the handlebars, or whatever. Are you going to stop, throw a leg over, and then clip in? Are you going to stay in motion and jump over the seat? Whatever the choice, practice it.
T2:
I really think that everyone, regardless of whether they have tri-shoes or regular cycling shoes and regardless of whether they pre-clipped their shoes for T1, should remove their shoes and pedal on top of them heading into Transition 2. It's a very easy way to get the free time. Run bare-foot to your run gear.
I've gone too long again. There are a lot of great tips out there for beginners, so I'll just say that the best thing you can do is obsess over every detail. Really think about what works for
you. How
you can go faster. What other people are doing is not always right. It's not a one-size-fits-all experience.
Enjoy it! And I hope this wasn't too boring.